text: Maximum path sum from top left to bottom right of a matrix passing through one of the given cells | C ++ program for the above approach ; Stores the maximum path sum from the cell ( 1 , 1 ) to ( N , M ) ; Stores the maximum path sum from the cell ( j , j ) to ( N , M ) ; Function to find the maximum path sum from the cell ( 1 , 1 ) to ( N , M ) ; Traverse the first row ; Traverse the first column ; Traverse the matrix ; Update the value of start [ i ] [ j ] ; Function to find the maximum path sum from the cell ( j , j ) to ( N , M ) ; Traverse the last row ; Traverse the last column ; Traverse the matrix ; Update the value of ending [ i ] [ j ] ; Function to find the maximum path sum from the top - left to the bottom right cell such that path contains one of the cells in the array coordinates [ ] [ ] ; Initialize the start and the end matrices ; Calculate the start matrix ; Calculate the end matrix ; Stores the maximum path sum ; Traverse the coordinates ; Update the value of ans ; Print the resultant maximum sum path value ; Drive Code
code: #include <iostream> NEW_LINE using namespace std ; int start [ 3 ] [ 3 ] ; int ending [ 3 ] [ 3 ] ; void calculateStart ( int n , int m ) { for ( int i = 1 ; i < m ; ++ i ) { start [ 0 ] [ i ] += start [ 0 ] [ i - 1 ] ; } for ( int i = 1 ; i < n ; ++ i ) { start [ i ] [ 0 ] += start [ i - 1 ] [ 0 ] ; } for ( int i = 1 ; i < n ; ++ i ) { for ( int j = 1 ; j < m ; ++ j ) { start [ i ] [ j ] += max ( start [ i - 1 ] [ j ] , start [ i ] [ j - 1 ] ) ; } } } void calculateEnd ( int n , int m ) { for ( int i = n - 2 ; i >= 0 ; -- i ) { ending [ i ] [ m - 1 ] += ending [ i + 1 ] [ m - 1 ] ; } for ( int i = m - 2 ; i >= 0 ; -- i ) { ending [ n - 1 ] [ i ] += ending [ n - 1 ] [ i + 1 ] ; } for ( int i = n - 2 ; i >= 0 ; -- i ) { for ( int j = m - 2 ; j >= 0 ; -- j ) { ending [ i ] [ j ] += max ( ending [ i + 1 ] [ j ] , ending [ i ] [ j + 1 ] ) ; } } } void maximumPathSum ( int mat [ ] [ 3 ] , int n , int m , int q , int coordinates [ ] [ 2 ] ) { for ( int i = 0 ; i < n ; ++ i ) { for ( int j = 0 ; j < m ; ++ j ) { start [ i ] [ j ] = mat [ i ] [ j ] ; ending [ i ] [ j ] = mat [ i ] [ j ] ; } } calculateStart ( n , m ) ; calculateEnd ( n , m ) ; int ans = 0 ; for ( int i = 0 ; i < q ; ++ i ) { int X = coordinates [ i ] [ 0 ] - 1 ; int Y = coordinates [ i ] [ 1 ] - 1 ; ans = max ( ans , start [ X ] [ Y ] + ending [ X ] [ Y ] - mat [ X ] [ Y ] ) ; } cout << ans ; } int main ( ) { int mat [ ] [ 3 ] = { { 1 , 2 , 3 } , { 4 , 5 , 6 } , { 7 , 8 , 9 } } ; int N = 3 ; int M = 3 ; int Q = 2 ; int coordinates [ ] [ 2 ] = { { 1 , 2 } , { 2 , 2 } } ; maximumPathSum ( mat , N , M , Q , coordinates ) ; }